PHYSICS PARTICLE. An Introductory Course of. Palash B. Pal. CRC Press. Saha Institute of Nuclear Physics. Kolkata, India. Taylor &.

Transcription

1 An Introductory Course of PARTICLE PHYSICS Palash B. Pal Saha Institute of Nuclear Physics Kolkata, India W CRC Press Taylor &. Francis Croup Boca Raton London New York CRC Press is an imprint of the & Francis Croup, an informa business Taylor A CHAPMAN & HALL BOOK

2 Contents List of Figures xvii List of Tables xxi Preface xxiii Notations xxvii 1 Scope of particle physics What are elementary particles? Inventory of elementary fermions Which properties? Fundamental interactions High energy physics Relativity and quantum theory Natural units Plan of the book 14 2 Relativistic kinematics Lorentz transformation equations Vectors and tensors on spacetime Velocity, momentum and energy Covariance Invariances and conservation laws Kinematics of decays Lifetime and time dilation Two-body decays Three-body decays Kinematics of scattering processes Center-of-mass frame Fixed-target frame 32 3 Symmetries and groups The role of symmetries Group theory Examples and classification Examples Classifications Generators Parameters and generators Algebra Representations Matrix and differential representations Irreducible representations 48 vii

3 viii Contents Kronecker product of representations Decomposition under a subgroup Lorentz group Generators and algebra Representations Extended Lorentz group and its representations Poincare' group 59 4 A brisk tour of quantum field theory Motivating quantum fields Plane wave solutions Scalar fields Vector fields Dirac fields Lagrangian Making Lorentz invariants with fields Invariants with scalar and vector fields Invariants involving Dirac fields Final recipe Lagrangians for free fields Noether currents and charges Quantum fields as operators States Interactions From Lagrangian to Feynman rules External lines Internal lines Vertices Other factors Feynman amplitude Calculation of decay rates General formula Two-body decays Three-body decays Calculation of cross-sections General formula Illustrative example Mandelstam variables Differential decay rates and cross-sections Angular distribution in the CM frame Invariant form of angular distribution Angular distribution in FT frame Other differentials Feynman diagrams that do not represent physical amplitudes Quantum electrodynamics Gauge invariance Global phase symmetry Local symmetry Charge conservation Interaction vertex Elastic scattering at second order Electron-electron scattering Electron-positron scattering Compton scattering Inelastic scattering at second order Pair creation and pair annihilation 130

4 Contents ix Muon pair production Scalar QED Multi-photon states Generalities Two-photon states Three-photon states Higher-order effects Electromagnetic form factors Form factors in non-relativistic limit Vertex function at one-loop Anomalous magnetic moment Parity and charge conjugation Discrete symmetries in classical electrodynamics Parity transformation of fields Parity invariance of a Lagrangian Free scalar fields Free photon field Free fermion fields Interacting fields Charge conjugation Nature of the transformation Free bosonic fields Free fermion fields Interacting fields Parity properties of particle states Intrinsic parity for bosons Intrinsic parity for fermions and antifermions Orbital parity Charge conjugation properties of particle states Multi-photon states Positronium Parity assignment of different particles Signature of parity violation Correlations in experiments Parity violating transitions Parity violating coupling with external fields Connection with field theory Consequences of charge conjugation symmetry CP symmetry Time-reversal and CPT symmetries Anti-unitary operators Definition Rules for working with operators Time reversal transformation on fields Free fields 19! Interactions CPT transformation on fields CPT theorem Consequences of CPT symmetry Time reversal transformation on states Signature of time reversal violation Isospin 8.1 Nuclear energy levels Isospin symmetry 202

5 x Contents 254 _ Group structure of isospin transformations Isospin representations Pions Isospin relations Forbidden processes Relative strengths Smushkevich's method G-parity Generalized Pauli principle Isospin and quarks Nucleons Pions More hadrons Pion-nucleon interaction Isospin breaking Baryon number Discovering particles Discoveries of electron, proton and neutron New particles in cosmic rays Accelerators Detectors Hadronic zoo Detecting short-lived particles Resonances Reconstruction of events Discovering leptons Overview of particle physics experiments Non-accelerator experiments Accelerator experiments SU(3) quark model 10.1 Strange quark Hypercharge Hypercharge and charge of hadrons Hypercharge and isospin SU(3) Some general properties of SU(iV) groups Fundamental representation Conjugate representation Examples of other representations Young tableaux Decompositions in a subgroup Mesons from three flavors of quarks Baryons from three flavors of quarks l/-spin and V-spin SU(3) breaking and mass relations Electromagnetic properties in SU(3) Fundamental interaction Baryon magnetic moments Electromagnetic mass differences Decays of hadrons Decays of members of pseudoscalar meson octet Decays of members of baryon octet Decays of members of baryon decuplet Decays of members of vector meson nonet Summary of conservation laws 293

6 Contents xi Color Symmetry of baryon states Generalized Pauli principle Non-abelian gauge theories Local SU(7V) invariance Gauge fields Transformation properties of gauge fields Field-strength tensor Pure gauge Lagrangian Mathematical interlude Free gauge Lagrangian Self-interaction of gauge bosons Quartic vertices of gauge bosons Cubic vertices of gauge bosons Fadeev-Popov ghosts Interaction of gauge bosons with other particles Quantum chromodynamics SU(3) of color Running parameters Why parameters run Running of QED coupling Beta function Running of the QCD coupling QCD Lagrangian Perturbative QCD Cross-sections involving quarks and gluons Jet production The 1/N expansion Lattice gauge theory Scope and basics Path integral Quantum field theory Euclidean on spacetime Quarks and gluons on a lattice Lattice action Fermion doubling problem Path integral on a lattice Correlation functions and physical o'oservables Continuum limit Confinement Asymptotic properties of color gauge fields Dual of field-strength tensor Topological invariants QCD vacuum Structure of hadrons Electron-proton elastic scattering Deep inelastic scattering Structure functions and charge distribution Scaling Partons Parton distribution functions Parton distribution and cross-section Fragmentation Scale dependence of parton distribution Quark masses 407

7 xji Contents Glueballs Fermi theory of weak interactions 410 _ 14.1 Four-fermion interaction Helicity and chirality Helicity Chirality Connection Neutrino helicity Weyl fermions Fierz transformations Scalar combinations Pseudoscalar combinations Invariant combinations with fields Elastic neutrino-electron scattering Inelastic neutrino-electron scattering Muon and tau decay Parity violation Problems with Fermi theory Intermediate vector bosons Spontaneous symmetry breaking Examples of spontaneous symmetry breaking Breaking a Zi symmetry Breaking a U(l) symmetry Breaking a non-abelian symmetry Goldstone theorem Interaction of Goldstone bosons Higgs mechanism Gauge boson mass Gauge fixing Unitary gauge Renormalizablity Standard electroweak model with leptons Chiral fermions and internal symmetries Leptons and the gauge group Symmetry breaking Gauge bosons and their masses Couplings of photon Gauge fixing Gauge interaction of fermions Yukawa sector Connection with Fermi theory Charged-current induced processes Neutral-current induced processes Processes induced by both types of currents Forward-backward asymmetry Electroweak interaction of hadrons Quarks in standard model Gauge interaction of quarks CKM matrix and its parametrization Yukawa interaction of quarks Leptonic decays of mesons Decay of charged pions Decay of charged kaons

8 Contents xiii Related processes Spin and parity of hadronic currents Selection rules for charged currents Semileptonic decays of mesons Neutral kaons Eigenstates in the neutral kaon sector Decays of neutral kaons into pions Kaon oscillations K\-K% mass difference Leptonic decays of neutral kaons Processes involving baryons Global symmetries of standard model Accidental symmetries Approximate symmetries Chiral symmetries Symmetries of massless Dirac Lagrangian Sigma model Currents and charges Chiral symmetry breaking PCAC and soft pion theorem Quark masses Chiral Lagrangians Anomalies Failure of Noether's theorem QCD anomaly of U(l)a Decay of neutral pions Anomaly cancellation for gauge currents Non-anomalous global symmetry Bosons of standard model Interactions among bosons Self-interaction among gauge bosons Self-interaction among scalars Gauge-scalar interactions Decay of gauge bosons Scattering of gauge bosons Equivalence theorem Custodial symmetry Loop corrections Oblique parameters Evaluation of T Higgs boson Elusiveness Theoretical bounds on mass Production Decay Hadrons involving heavy quark flavors 20.1 Charm quark and charmed hadrons Prediction of charm quark Discovery of charmonium Flavor SU(4) Discovery of other charm-containing hadrons Decay of mesons with charm quark Decay of baryons with charm quark Bottom quark 606

9 xiv Contents _ Discovery of bottom-containing hadrons Decay of bottom-containing hadrons Neutral meson-antimeson systems Top quark Quark masses Heavy quark effective theory Symmetries Hadron fields Consequences CP violation CP violation and complex parameters Kobayashi-Maskawa theory of CP violation Rephasing invariant formulation CP-violating decays of kaons Observables and experimental results Identifying sources of CP violation CP violation in semileptonic decays CP violation in decays into two pions Standard model estimates Other signals of CP violation Decays of mesons involving heavier quarks CP-violating correlations Electric dipole moment Unitarity triangle CP violation and T violation Strong CP problem Effective 0-parameter Physical effects of Can 6 be irrelevant? Neutrino mass and lepton _ mixing 22.1 Simple extension of standard model Neutrino oscillation Theoretical analysis Experimental data Matter effects Summary Majorana fermions Definition Feynman rules Consequences of lepton mixing Lepton flavor violation CP violation in leptonic sector Lepton number violation Neutrinoless double beta decay Lepton to antilepton conversion Models of neutrino mass Adding singlet neutrinos Effective Lagrangian for neutrino mass Beyond the standard model Shortcomings of standard model Left-right symmetric model Grand unified theories Horizontal symmetry Supersymmetry 711

10 Contents xv 23.6 Higher dimensional theories String theory 714 Appendix A Units and constants 717 Appendix B Short summary of particle properties 719 Appendix C Timeline of major advances in particle physics 724 Appendix D Properties of spacetime 727 D.l Metric tensor 727 D.2 Levi-Civita symbol 728 D.2.1 Contraction properties 729 D.2.2 Transformation properties 729 D.2.3 Spatial antisymmetric tensor 731 Appendix E Clebsch-Gordan co-efficients 732 Appendix F Dirac matrices and spinors 735 P.l Dirac matrices 735 F.l.l Basic properties 735 F.1.2 Associated matrices 737 F.1.3 Contraction formulas 738 F.1.4 Trace formulas 738 F.1.5 Strings of Dirac matrices 741 F.1.6 A property of the matrix C 742 F.2 Dirac spinors 743 F.2.1 Plane wave solutions of Dirac equation 743 F.2.2 Normalization of spinors 745 F.2.3 Conjugation properties 745 F.2.4 Result of 70 multiplying the spinors 746 F.2.5 Result of 75 multiplying the spinors 747 F.2.6 Spin sums 749 F.2.7 Projection matrices on spinors 749 F. 3 Bilinears 752 F.3.1 Gordon identity 752 F.3.2 Squaring amplitudes 753 F.3.3 Non-relativistic reduction 754 Appendix G Evaluation of loop integrals 756. G. l Introducing Feynman parameters 756 G.2 Reduction to invariant integrals 758 G.3 Wick rotation 759 G.4 Angular integration 761 G.5 Integration over the magnitude 761 G. 6 Divergent integrals 762 Appendix H Feynman rules for standard model 766 H. l External lines 766 H.2 Propagators 766 H.3 Vertices 767 H.3.1 Vertices in gauge sector 767 H.3.2 Gauge bosons and Higgs bosons 769 H.3.3 Scalar self-interactions 770 H.3.4 Vertices involving fermions 770 Appendix I Books and other reviews. 772

11 xvi Contents Appendix J Answers to selected exercises 775 Index 777